Solve for $x$. Enter the solutions from least to greatest. $(x +6)(-x +1)=0$ $\text{lesser }x = $
For any two expressions $A$ and $B$ : If $A\cdot B=0$ then either $A=0$ or $B=0$. This is called the zero product property. In our case, $(x +6)(-x +1)=0$. So either $(x +6)=0$ or $(-x +1)=0$ : $\begin{aligned} (1)&&x +6&=0 \\\\ &&x&=-6 \end{aligned}$ $\begin{aligned} (2)&&-x +1&=0 \\\\ &&-x &= -1 \\\\ &&x&=1 \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= -6 \\\\ \text{greater } x &= 1 \end{aligned}$